{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# --> Import standard functions from numpy.\n",
    "import numpy as np\n",
    "from numpy.random import normal\n",
    "\n",
    "# --> Import matplotlib and set related parameters.\n",
    "import matplotlib.pyplot as plt\n",
    "fig_width = 12\n",
    "\n",
    "# --> Import SciPy utility functions for linear dynamical systems.\n",
    "from scipy.signal import lti\n",
    "from scipy.signal import dlti, dlsim\n",
    "\n",
    "# --> Import standard linear algebra functions from SciPy.\n",
    "from scipy.linalg import norm\n",
    "\n",
    "# --> Import various DMD algorithms available in PyDMD.\n",
    "from pydmd import DMD, OptDMD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 8 : Comparison of various DMD algorithms\n",
    "\n",
    "In this tutorial, we perform a thorough comparison of various DMD algorithms available in PyDMD, namely:\n",
    "- the original DMD algorithm proposed by [Schmid (*J. Fluid Mech.*, 2010)](https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/dynamic-mode-decomposition-of-numerical-and-experimental-data/AA4C763B525515AD4521A6CC5E10DBD4), see `DMD`\n",
    "- the optimal closed-form solution given by [Héas & Herzet (*arXiv*, 2016)](https://arxiv.org/abs/1610.02962), see `OptDMD`.\n",
    "\n",
    "For that purpose, different test cases are considered in order to assess the accuracy, the computational efficiency and the generalization capabilities of each method. The system we'll consider throughout this notebook is that of a chain of slightly damped 1D harmonic oscillators with nearest-neighbours coupling. Defining the state-vector as\n",
    "\n",
    "$$\n",
    "    \\mathbf{x} = \\begin{bmatrix} \\mathbf{q} & \\mathbf{p} \\end{bmatrix}^T,\n",
    "$$\n",
    "\n",
    "where $\\mathbf{q}$ is the position and $\\mathbf{p}$ is the momentum, our linear system can be written as\n",
    "\n",
    "$$\n",
    "    \\displaystyle \\frac{\\mathrm{d}}{\\mathrm{d}t} \\begin{bmatrix} \\mathbf{q} \\\\ \\mathbf{p} \\end{bmatrix} = \\begin{bmatrix} \\mathbf{0} & \\mathbf{I} \\\\ -\\mathbf{K} & -\\mathbf{G} \\end{bmatrix} \\begin{bmatrix} \\mathbf{q} \\\\ \\mathbf{p} \\end{bmatrix},\n",
    "$$\n",
    "\n",
    "with $\\mathbf{K}$ and $\\mathbf{G}$ being the stiffness and friction matrices, respectively. It must be emphasized that, because we consider $N=50$ identifical oscillators, this system does not exhibit low-rank dynamics. It will nonetheless enable us to further highlight the benefits of using the optimal solution proposed by [Héas & Herzet (arXiv, 2016)](https://arxiv.org/abs/1610.02962) as opposed to the other algorithms previously available in PyDMD.\n",
    "\n",
    "Three different test cases will be considered :\n",
    "- fitting a DMD model using a single long time-series,\n",
    "- fitting a DMD model using a short burst,\n",
    "- fitting a DMD model using an ensemble of short bursts.\n",
    "\n",
    "For each case, the reconstruction error on the training dataset used to fit the model will be reported along with the error on an ensemble of testing datasets as to assess the generalization capabilities of these various DMD models. The following two cells build the discrete linear time invariant (LTI) state space model for our system. It is this particular system, hereafter denoted `dsys`, that will be used throughout this notebook to generate both the training and testing datasets. For more details about SciPy implementation of LTI systems, interested readers are refered to the [`scipy.signal`](https://docs.scipy.org/doc/scipy/reference/signal.html#discrete-time-linear-systems) module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def harmonic_oscillators(N=10, omega=0.1, alpha=0.2, gamma=0.05, dt=1.0):\n",
    "    \n",
    "    \"\"\"\n",
    "    This function builds the discrete-time model of a chain of N coupled\n",
    "    weakly damped harmonic oscillators. All oscillators are identical to\n",
    "    one another and have a nearest-neighbour coupling.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    N : integer\n",
    "        The number of oscillators forming the chain (default 10).\n",
    "        \n",
    "    omega : float\n",
    "            The natural frequency of the base oscillator (default 0.1).\n",
    "            \n",
    "    alpha : float\n",
    "            The nearest-neighbour coupling strength (default 0.2).\n",
    "            \n",
    "    gamma : float\n",
    "            The damping parameter (default 0.05).\n",
    "            \n",
    "    dt    : float\n",
    "            The sampling period for the continuous-to-discrete time conversion (default 1.0).\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    dsys :  scipy.signal.dlti\n",
    "            The corresponding discrete-time state-space model.\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    # --> Miscellaneous imports.\n",
    "    from scipy.sparse import diags, identity, bmat, block_diag\n",
    "    \n",
    "    # --> Build the stiffness matrix.\n",
    "    K_ii = np.ones((N,)) * (omega**2/2.0 + alpha) # Self-coupling.\n",
    "    K_ij = np.ones((N-1,)) * (-alpha/2.0) # Nearest-neighbor coupling.\n",
    "    K = diags([K_ij, K_ii, K_ij], offsets=[-1, 0, 1]) # Assembles the stiffness matrix.\n",
    "    \n",
    "    # --> Build the friction matrix.\n",
    "    G = gamma * identity(N)\n",
    "    \n",
    "    # --> Build the dynamic matrix.\n",
    "    A = bmat([[None, identity(N)], [-K, -G]])\n",
    "    \n",
    "    # --> Build the control matrix.\n",
    "    B = bmat([[0*identity(N)], [identity(N)]])\n",
    "    \n",
    "    # --> Build the observation matrix.\n",
    "    C = identity(2*N)\n",
    "    \n",
    "    # --> Build the feedthrough matrix.\n",
    "    D = bmat([[0*identity(N)], [0*identity(N)]])\n",
    "    \n",
    "    # --> SciPy continuous-time LTI object.\n",
    "    sys = lti(A.toarray(), B.toarray(), C.toarray(), D.toarray())\n",
    "    \n",
    "    # --> Return the discrete-time equivalent.\n",
    "    return sys.to_discrete(dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# --> Get the discrete-time LTI model.\n",
    "N = 50 # Number of oscillators (each has 2 degrees of freedom so the total size of the system is 2N).\n",
    "dsys = harmonic_oscillators(N=N) # Build the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Case 1 : Using a single long time-series to fit a DMD model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# --> Training initial condition.\n",
    "x0_train = normal( loc=0.0, scale=1.0, size=(dsys.A.shape[1]) )\n",
    "\n",
    "# --> Run simulation to generate dataset.\n",
    "t, _, x_train = dlsim(dsys, np.zeros((2000, dsys.inputs)), x0=x0_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_training_dataset(t, x_train):\n",
    "    \n",
    "    \"\"\"\n",
    "    This is a simple utility function to plot the time-series forming our training dataset.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    \n",
    "    t : array-like, shape (n_samples,)\n",
    "        The time instants.\n",
    "    x_train : array-like, shape (n_samples, n_dof)\n",
    "        The time-series of our system.\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    # --> Setup the figure.\n",
    "    fig, axes = plt.subplots( 1, 2, sharex=True, figsize=(fig_width, fig_width/6) )\n",
    "\n",
    "    # --> Plot the oscillators' positions.\n",
    "    axes[0].plot( t, x_train[:, :dsys.inputs], alpha=0.5)\n",
    "\n",
    "    # --> Add decorators.\n",
    "    axes[0].set_ylabel(r\"$q_i[k]$\")\n",
    "    \n",
    "    # --> Plot the oscillators'velocities.\n",
    "    axes[1].plot( t, x_train[:, dsys.inputs:], alpha=0.5 )\n",
    "\n",
    "    # --> Add decorators.\n",
    "    axes[1].set( xlim=(t.min(), t.max()), xlabel=r\"k\", ylabel=r\"p_i[k]$\" )\n",
    "    \n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_training_dataset(t, x_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now fit our models, namely vanilla DMD (Schmid, *J. Fluid Mech.*, 2010) and the closed-form solution DMD (Héas & Herzet, *arXiv*, 2016)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rank_sensitvity(dsys, x_train, n_test=100):\n",
    "    \n",
    "    \"\"\"\n",
    "    This function using the generated training dataset to fit DMD and OptDMD models of increasing rank.\n",
    "    It also computes the test error on an ensemble of testing dataset to get a better estimation of the\n",
    "    generalization capabilities of the fitted models.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    \n",
    "    dsys : scipy.signal.dlti\n",
    "        The discrete LTI system considered.\n",
    "        \n",
    "    x_train : array-like, shape (n_features, n_samples)\n",
    "        The training dataset.\n",
    "        NOTE : It is transposed compared to the output of dsys.\n",
    "        \n",
    "    n_test : int\n",
    "        The number of testing datasets to be generated.\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    \n",
    "    dmd_train_error : array-like, shape (n_ranks,)\n",
    "        The reconstruction error of the DMD model on the training data.\n",
    "        \n",
    "    dmd_test_error : array-like, shape (n_ranks, n_test)\n",
    "        The reconstruction error of the DMD model on the various testing datasets.\n",
    "        \n",
    "    optdmd_train_error : array-like, shape (n_ranks,)\n",
    "        The reconstruction error of the OptDMD model on the training data.\n",
    "        \n",
    "    optdmd_test_error : array-like, shape (n_ranks, n_test)\n",
    "        The reconstruction error of the OptDMD model on the various testing datasets.\n",
    "        \n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    # -->\n",
    "    dmd_train_error, optdmd_train_error = list(), list()\n",
    "    dmd_test_error, optdmd_test_error = list(), list()\n",
    "\n",
    "            \n",
    "    # --> Split the training data into input/output snapshots.\n",
    "    y_train, X_train = x_train[:, 1:], x_train[:, :-1]\n",
    "    \n",
    "    for rank in range(1, dsys.A.shape[0]+1):\n",
    "        \n",
    "        # --> Fit the DMD model (Schmid's algorithm)\n",
    "        dmd = DMD(svd_rank=rank).fit(x_train)\n",
    "        \n",
    "        # --> Fit the DMD model (optimal closed-form solution)\n",
    "        optdmd = OptDMD(svd_rank=rank, factorization=\"svd\").fit(x_train)\n",
    "\n",
    "        # --> One-step ahead prediction using both DMD models.\n",
    "        y_predict_dmd = dmd.predict(X_train)\n",
    "        y_predict_opt = optdmd.predict(X_train)\n",
    "\n",
    "        # --> Compute the one-step ahead prediction error.\n",
    "        dmd_train_error.append( norm(y_predict_dmd-y_train)/norm(y_train) )\n",
    "        optdmd_train_error.append( norm(y_predict_opt-y_train)/norm(y_train) ) \n",
    "        \n",
    "        # --> Evaluate the error on test data.\n",
    "        dmd_error, optdmd_error = list(), list()\n",
    "        for _ in range(n_test):\n",
    "            # --> Test initial condition.\n",
    "            x0_test = normal( loc=0.0, scale=1.0, size=(dsys.A.shape[1]) )\n",
    "\n",
    "            # --> Run simulation to generate dataset.\n",
    "            t, _, x_test = dlsim(dsys, np.zeros((250, dsys.inputs)), x0=x0_test)\n",
    "            \n",
    "            # --> Split the training data into input/output snapshots.\n",
    "            y_test, X_test = x_test.T[:, 1:], x_test.T[:, :-1]\n",
    "\n",
    "            # --> One-step ahead prediction using both DMD models.\n",
    "            y_predict_dmd = dmd.predict(X_test)\n",
    "            y_predict_opt = optdmd.predict(X_test)\n",
    "\n",
    "            # --> Compute the one-step ahead prediction error.\n",
    "            dmd_error.append( norm(y_predict_dmd-y_test)/norm(y_test) )\n",
    "            optdmd_error.append( norm(y_predict_opt-y_test)/norm(y_test) ) \n",
    "\n",
    "        # --> Store the error for rank i DMD.\n",
    "        dmd_test_error.append( np.asarray(dmd_error) )\n",
    "        optdmd_test_error.append( np.asarray(optdmd_error) )\n",
    "\n",
    "    # --> Complete rank-sensitivity.\n",
    "    dmd_test_error = np.asarray(dmd_test_error)\n",
    "    optdmd_test_error = np.asarray(optdmd_test_error)\n",
    "    \n",
    "    dmd_train_error = np.asarray(dmd_train_error)\n",
    "    optdmd_train_error = np.asarray(optdmd_train_error)\n",
    "    \n",
    "    return dmd_train_error, dmd_test_error, optdmd_train_error, optdmd_test_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_rank_sensitivity(dmd_train_error, dmd_test_error, optdmd_train_error, optdmd_test_error):\n",
    "    \n",
    "    \"\"\"\n",
    "    Simple utility function to plot the results from the rank sensitivity analysis.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    \n",
    "    dmd_train_error : array-like, shape (n_ranks,)\n",
    "        The reconstruction error of the DMD model on the training data.\n",
    "        \n",
    "    dmd_test_error : array-like, shape (n_ranks, n_test)\n",
    "        The reconstruction error of the DMD model on the various testing datasets.\n",
    "        \n",
    "    optdmd_train_error : array-like, shape (n_ranks,)\n",
    "        The reconstruction error of the OptDMD model on the training data.\n",
    "        \n",
    "    optdmd_test_error : array-like, shape (n_ranks, n_test)\n",
    "        The reconstruction error of the OptDMD model on the various testing datasets.\n",
    "\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    # --> Generate figure.\n",
    "    fig, axes = plt.subplots( 1, 2, figsize=(fig_width, fig_width/4), sharex=True, sharey=True )\n",
    "    \n",
    "    # --> Misc.\n",
    "    rank = np.arange(1, dmd_test_error.shape[0]+1)\n",
    "    \n",
    "    #####\n",
    "    #####    TRAINING ERROR\n",
    "    #####\n",
    "    \n",
    "    # --> Plot the vanilla DMD error.    \n",
    "    axes[0].plot( rank, dmd_train_error )\n",
    "    # --> Plot the OptDMD error.\n",
    "    axes[0].plot( rank, optdmd_train_error, ls=\"--\" )\n",
    "    # --> Add decorators.\n",
    "    axes[0].set(\n",
    "        xlabel=r\"Rank of the DMD model\", ylabel=r\"Normalized error\", title=r\"Training dataset\"\n",
    "    )\n",
    "    axes[0].grid(True)\n",
    "    \n",
    "    #####\n",
    "    #####     TESTING ERROR\n",
    "    #####\n",
    "    \n",
    "    # --> Plot the vanilla DMD error.\n",
    "    axes[1].plot( rank, np.mean(dmd_test_error, axis=1), label=r\"Regular DMD\" )\n",
    "    axes[1].fill_between(\n",
    "        rank,\n",
    "        np.mean(dmd_test_error, axis=1) + np.std(dmd_test_error, axis=1),\n",
    "        np.mean(dmd_test_error, axis=1) - np.std(dmd_test_error, axis=1),\n",
    "        alpha=0.25,\n",
    "    )\n",
    "    # --> Plot the OptDMD error.\n",
    "    axes[1].plot( rank, np.mean(optdmd_test_error, axis=1), ls=\"--\", label=r\"Optimal DMD\" )\n",
    "    axes[1].fill_between(\n",
    "        rank,\n",
    "        np.mean(optdmd_test_error, axis=1) + np.std(optdmd_test_error, axis=1),\n",
    "        np.mean(optdmd_test_error, axis=1) - np.std(optdmd_test_error, axis=1),\n",
    "        alpha=0.25,\n",
    "    )\n",
    "    # --> Add decorators.\n",
    "    axes[1].set(\n",
    "        xlim = (0, rank.max()), xlabel=r\"Rank of the DMD model\",\n",
    "        ylim=(0, 1),\n",
    "        title=r\"Testing dataset\"\n",
    "    )\n",
    "    axes[1].grid(True)\n",
    "    axes[1].legend(loc=0)\n",
    "    \n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# --> Run the rank-sensitivity analysis.\n",
    "output = rank_sensitvity(dsys, x_train.T)\n",
    "\n",
    "# --> Keep for later use.\n",
    "long_time_series_optdmd_train, long_time_series_optdmd_test = output[2], output[3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --> Plot the results.\n",
    "plot_rank_sensitivity(*output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Case 2 : Using a short burst to fit a DMD model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --> Training initial condition.\n",
    "x0_train = normal( loc=0.0, scale=1.0, size=(dsys.A.shape[1]) )\n",
    "\n",
    "# --> Run simulation to generate dataset.\n",
    "t, _, x_train = dlsim(dsys, np.zeros((100, dsys.inputs)), x0=x0_train)\n",
    "\n",
    "# --> Plot the corresponding training data.\n",
    "plot_training_dataset(t, x_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# --> Run the rank-sensitivity analysis.\n",
    "output = rank_sensitvity(dsys, x_train.T)\n",
    "\n",
    "# --> Keep for later use.\n",
    "short_time_series_optdmd_train, short_time_series_optdmd_test = output[2], output[3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --> Plot the results.\n",
    "plot_rank_sensitivity(*output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Case 3 : Fitting a DMD model using an ensemble of trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_ensemble_time_series(dsys, n_traj, len_traj):\n",
    "    \n",
    "    \"\"\"\n",
    "    Utility function to generate a training dataset formed by an ensemble of time-series.\n",
    "    \n",
    "    Parameters\n",
    "    -----------\n",
    "    \n",
    "    dsys : scipy.signal.dlti\n",
    "        The discrete LTI system considered.\n",
    "        \n",
    "    n_traj : int\n",
    "        The numbr of trajectories forming our ensemble.\n",
    "        \n",
    "    len_traj : int\n",
    "        The length of each time-series.\n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    \n",
    "    X : array-like, shape (n_features, n_samples)\n",
    "        The input to the system.\n",
    "        \n",
    "    Y : array-like, shape (n_features, n_samples)\n",
    "        The output of the system.\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    for i in range(n_traj):\n",
    "        # --> Training initial condition.\n",
    "        x0_train = normal(loc=0.0,scale=1.0,size=(dsys.A.shape[1]))\n",
    "\n",
    "        # --> Run simulation to generate dataset.\n",
    "        t, _, x = dlsim(dsys, np.zeros((len_traj, dsys.inputs)), x0=x0_train)\n",
    "\n",
    "        # --> Store the data.\n",
    "        if i == 0:\n",
    "            X, Y = x.T[:, :-1], x.T[:, 1:]\n",
    "        else:\n",
    "            X, Y = np.c_[X, x.T[:, :-1]], np.c_[Y, x.T[:, 1:]]\n",
    "    return X, Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rank_sensitvity_bis(dsys, X, Y, n_test=100):\n",
    "    \n",
    "    \"\"\"\n",
    "    Same as before but for the ensemble training. Note that no DMD model is fitted, only OptDMD.\n",
    "    \"\"\"\n",
    "    \n",
    "    optdmd_train_error, optdmd_test_error = list(), list()\n",
    "    \n",
    "    # --> Fit a DMD model for each possible rank.\n",
    "    for rank in range(1, dsys.A.shape[0]+1):\n",
    "        \n",
    "        # --> Fit the DMD model (optimal closed-form solution)\n",
    "        optdmd = OptDMD(svd_rank=rank, factorization=\"svd\").fit(X, Y)\n",
    "\n",
    "        # --> One-step ahead prediction using both DMD models.\n",
    "        y_predict_opt = optdmd.predict(X)\n",
    "\n",
    "        # --> Compute the one-step ahead prediction error.\n",
    "        optdmd_train_error.append( norm(y_predict_opt-Y)/norm(Y) ) \n",
    "        \n",
    "        # --> Evaluate the error on test data.\n",
    "        optdmd_error = list()\n",
    "        for _ in range(n_test):\n",
    "            # --> Test initial condition.\n",
    "            x0_test = normal(loc=0.0,scale=1.0,size=(dsys.A.shape[1]))\n",
    "\n",
    "            # --> Run simulation to generate dataset.\n",
    "            t, _, x_test = dlsim(dsys, np.zeros((250, dsys.inputs)), x0=x0_test)\n",
    "            \n",
    "            # --> Split the training data into input/output snapshots.\n",
    "            y_test, X_test = x_test.T[:, 1:], x_test.T[:, :-1]\n",
    "\n",
    "            # --> One-step ahead prediction using both DMD models.\n",
    "            y_predict_opt = optdmd.predict(X_test)\n",
    "\n",
    "            # --> Compute the one-step ahead prediction error.\n",
    "            optdmd_error.append( norm(y_predict_opt-y_test)/norm(y_test) ) \n",
    "\n",
    "        # --> Store the error for rank i DMD.\n",
    "        optdmd_test_error.append( np.asarray(optdmd_error) )\n",
    "\n",
    "    # --> Complete rank-sensitivity.\n",
    "    optdmd_test_error = np.asarray(optdmd_test_error)\n",
    "    optdmd_train_error = np.asarray(optdmd_train_error)\n",
    "    \n",
    "    return optdmd_train_error, optdmd_test_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_rank_sensitivity_bis(\n",
    "    short_time_series_optdmd_train, short_time_series_optdmd_test,\n",
    "    long_time_series_optdmd_train, long_time_series_optdmd_test,\n",
    "    optdmd_train_error, optdmd_test_error\n",
    "):\n",
    "\n",
    "    \"\"\"\n",
    "    Same as before for this second rank sensitivity analysis.\n",
    "    \"\"\"\n",
    "    \n",
    "    # --> Generate figure.\n",
    "    fig, axes = plt.subplots( 1, 2,  figsize=(fig_width, fig_width/4), sharey=True, sharex=True )\n",
    "    \n",
    "    # --> Misc.\n",
    "    rank = np.arange(1, optdmd_train_error.shape[0]+1)\n",
    "\n",
    "    #####\n",
    "    #####     TRAINING ERROR\n",
    "    #####\n",
    "    \n",
    "    # --> Training error using a short time-series to fit the model.\n",
    "    axes[0].plot( rank, short_time_series_optdmd_train )\n",
    "    # --> Training error using a long time-series to fit the model.\n",
    "    axes[0].plot( rank, long_time_series_optdmd_train )\n",
    "    # --> Training error using an ensemble of short time-series to fit the model.\n",
    "    axes[0].plot( rank, optdmd_train_error )\n",
    "\n",
    "    # --> Add decorators.\n",
    "    axes[0].set(\n",
    "        xlim=(0, rank.max()), ylim=(0, 1),\n",
    "        xlabel=r\"Rank of the DMD model\", ylabel=r\"Normalized error\",\n",
    "        title=r\"Training dataset\"\n",
    "    )\n",
    "    axes[0].grid(True)\n",
    "\n",
    "    #####\n",
    "    #####     TESTING ERROR\n",
    "    #####\n",
    "    \n",
    "    # --> Testing error for the model fitted with a short time-series.\n",
    "    axes[1].plot( rank, np.mean(short_time_series_optdmd_test, axis=1), label=r\"Short time-series\" )\n",
    "    axes[1].fill_between(\n",
    "        rank,\n",
    "        np.mean(short_time_series_optdmd_test, axis=1) + np.std(short_time_series_optdmd_test, axis=1),\n",
    "        np.mean(short_time_series_optdmd_test, axis=1) - np.std(short_time_series_optdmd_test, axis=1),\n",
    "        alpha=0.25,\n",
    "    )\n",
    "\n",
    "    # --> Testing error for the model fitted with a long time-series.\n",
    "    axes[1].plot( rank, np.mean(long_time_series_optdmd_test, axis=1), label=r\"Long time-series\" )\n",
    "    axes[1].fill_between(\n",
    "        rank,\n",
    "        np.mean(long_time_series_optdmd_test, axis=1) + np.std(long_time_series_optdmd_test, axis=1),\n",
    "        np.mean(long_time_series_optdmd_test, axis=1) - np.std(long_time_series_optdmd_test, axis=1),\n",
    "        alpha=0.25,\n",
    "    )\n",
    "    \n",
    "    # --> Testing error for the model fitted using an ensemble of trajectories.\n",
    "    axes[1].plot( rank, np.mean(optdmd_test_error, axis=1), label=r\"Ensemble\" )\n",
    "    axes[1].fill_between(\n",
    "        rank,\n",
    "        np.mean(optdmd_test_error, axis=1) + np.std(optdmd_test_error, axis=1),\n",
    "        np.mean(optdmd_test_error, axis=1) - np.std(optdmd_test_error, axis=1),\n",
    "        alpha=0.25,\n",
    "    )\n",
    "\n",
    "    # --> Add decorators.\n",
    "    axes[1].set(\n",
    "        xlim=(0, rank.max()), ylim=(0, 1),\n",
    "        xlabel=r\"Rank of the DMD model\", title=r\"Testing dataset\"\n",
    "    )\n",
    "    axes[1].grid(True)\n",
    "    axes[1].legend(loc=0)\n",
    "\n",
    "    return"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Case 3.1 : Small ensemble"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# --> Number of trajectories and length.\n",
    "n_traj, len_traj = 10, 10\n",
    "X, Y = generate_ensemble_time_series(dsys, n_traj, len_traj)\n",
    "\n",
    "# --> Run the rank-sensitivity analysis.\n",
    "optdmd_train_error, optdmd_test_error = rank_sensitvity_bis(dsys, X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rank_sensitivity_bis(\n",
    "    short_time_series_optdmd_train, short_time_series_optdmd_test,\n",
    "    long_time_series_optdmd_train, long_time_series_optdmd_test,\n",
    "    optdmd_train_error, optdmd_test_error\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Case 3.2 : Large ensemble"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# --> Number of trajectories and length.\n",
    "n_traj, len_traj = 200, 10\n",
    "X, Y = generate_ensemble_time_series(dsys, n_traj, len_traj)\n",
    "\n",
    "# --> Run the rank-sensitivity analysis.\n",
    "optdmd_train_error, optdmd_test_error = rank_sensitvity_bis(dsys, X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rank_sensitivity_bis(\n",
    "    short_time_series_optdmd_train, short_time_series_optdmd_test,\n",
    "    long_time_series_optdmd_train, long_time_series_optdmd_test,\n",
    "    optdmd_train_error, optdmd_test_error\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "These various tests show that:\n",
    "- The models fitted using the new `OptDMD` consistently have smaller errors both on the training and testing datasets as compared to the regular `DMD`, no matter whether one has few data or a lot of data.\n",
    "- When a single time-series is used, both `DMD` and `OptDMD` models tend to actually overfit the training data. Indeed, a zero reconstruction error can be achieved for a low-rank model on the training data. The same models however poorly generalize to new testing data.\n",
    "- In order to prevent this overfitting problem, using an ensemble of bursts (i.e. short time-series) to fit the model appear to be extremely beneficial. In this case, the model's error on the testing dataset is of the same order as the error on the training one. Using such an ensemble of trajectories is moreover data-efficient : for a given reconstruction error, `OptDMD` models fitted using an ensemble of trajectories require actually less data than models fitted using a single time-series."
   ]
  }
 ],
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